Pion couplings of theΔ(1232)

Abstract

We calculate the strong couplings of pions to the ∆(1232) resonance using a QCD parameterization method that includes in addition to the usual one-quark also two-quark and previously uncalculated three-quark operators. We find that three-quark operators are necessary to obtain results consistent with the data and other QCD based baryon structure models. Our results are also in quantitative agreement with a model employing large D state admixtures to the N and ∆ wave functions indicating that the πN and π∆ couplings are sensitive to the spatial shape of these baryons.

Ernest Henley and the shape of baryons

“…( 8) is modified. It turned out that threequark terms have a major effect on the π∆∆ coupling and the reduction of the π∆∆ coupling obtained in second order is more than compensated by the inclusion of third order symmetry breaking term [19]. We also found an interesting connection between the πN N , πN ∆ and π∆∆ couplings and the shape of the N and ∆.…”

“…For the strong pion-baryon couplings one-, two-, and three-quark axial vector operators are defined as [7,19]…”

“…Baryon First order Second order p level matrix elements must be divided by baryon level spin and isospin Clebsch-Gordan coefficients [7,19]. Table II lists the various couplings in terms of f , the π 0 p coupling constant, to first order and to second order with and without the inclusion of the SU(3) flavor symmetry breaking parameter r = m u /m s .…”

A unified approach to hadron phenomenology at zero and finite temperatures in a hard-wall AdS/QCD model

“…(32) that ψ 0 = 0 for static spin-3/2 particles. 8 For g π∆ ∆ , the experimental data [39] give the range 1.1-30, and the predictions of other models (such as 1/N c expansion [40,41], QCD sum rule [38], and QCD parameterization method [42]) varies from 12 to 24.…”

Scattering of decuplet baryons in chiral effective field theory

“…Unfortunately, unlike the N Nπ and N Δπ coupling constants, the value for f ΔΔπ is not constrained by experimental information. A wide range of values for the ΔΔπ coupling constant can be found in the literature [47,48,57,[69][70][71][72]. In a variety of calculations the quark-model value [57] is used which amounts to f ΔΔπ = f N Nπ /5 [50] for the normalization of the spin and isospin operators as defined in Appendix [73] for m π ≈ 300 MeV.…”